You can do a lot more than that. You can craft, you can collect, you can explore, you can try using skills you rarely -- if ever -- used before, you can read all the in-game written lore items that you can find, you can observe the actions of npc's, you can study the stars, you can pretend that battles you are having (or places you are exploring) have additional levels of interest to your character, etc.
Really, it's up to you. The reason you leave the game on, to specifically answer your question, is because it provides a wonderful experience in its own right and it provides a canvas of activities over which you can layer your own thoughts and ideas. It's hard to explain to a non-rp'er, but if you can get into a game it becomes a lot more than just the pixels on the screen. How you accomplish that is up to you.
Everyone knows crafting breaks the game. So either you craft and break the game, or you craft and don't use the crafted items... lol so much for crafting :/
Collect, yes. Did that through normal play. Few insect jars here and there to decorate my home, the unique items. Purely decorative but it's something I did enjoy first couple of times.
I covered explore under cave and abandoned forts. You can only explore same place so many times.
Different skills fall under seven different characters.
Observe the actions of the NPC... what? Watching Ysolda being jelly of Nazeem's farm is worth watching after once?
If I were to use my own thoughts to build a story, I prefer a clean canvas

Really, the only roleplaying you can do outside of character build is murder, or go to caves. Unless you think having handful of insects in jars qualify as enough material to roleplay a entomologist

If I didn't roleplay this game would've gave out after 100 hours. Roleplaying got me another 100 or so, but the roleplaying option is so pitifully limited. I think you are the one who has been missing out on good solid roleplaying mechanics to find this game a good platform to roleplay upon.
These are more points I was trying to get at. You are only limited by your imagination.
One of my builds is an alchemist. For example.
I can daydream just fine without a game telling me what to think about